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The bending with large deflection of plates due to severe loads is frequently encountered in various modern engineering fields. Due to its severe nonlinearity, it is notoriously difficult to find a highly accurate solution for the bending of plates subjected to extreme large loads, especially for concentrated loads which will lead to a singular bending moment. In this study, the wavelet multiresolution interpolation Galerkin method is utilized to solve the highly coupled and nonlinear Von Karman equation for thin circular plates with various types of boundary conditions and external loads. In such a method, the unknown functions and nonlinear terms are represented by the wavelet multiresolution interpolation independently. Namely, they are approximated by their respective projections onto the same wavelet space. Moreover, this discretization process is as simple as that in solving linear problems and only common two-term connection coefficients are requested. In addition, all matrices in the resulting nonlinear discrete system are independent of unknown node values and lead to high efficiency in the calculation of the residual and Jacobian matrices needed in Newton's method, which does not require numerical integration. Numerical results demonstrate that the proposed wavelet multiresolution method is of capacity for solving geometrically nonlinear problems with singularity of thin circular plates, and has higher accuracy and lower computational cost than many existing methods. Moreover, a trivial initial guess, such as zero, can always lead to a convergent solution in very few iterations in Newton's method, showing an excellent convergence and stability in solving highly nonlinear problems.

Wavelet Multiresolution Interpolation; Geometrical nonlinearity; Concentrated Load; Circular Plate